منابع مشابه
A Quadratic Eigenvalue Problem
Let P, Q be compact selfadjoint operators in a Hilbert space. It is proven that the characteristic and associated vectors of the quadratic eigenvalue problem, x=\Px + (\¡X)Qx, form a Riesz basis for the cartesian product of the closure of the range of P and the closure of the range of Q. 1. Investigations in the theory of hydrodynamic stability (cf. [3, Chapter X] ; [8]) lead to the search for ...
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We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.
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The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit the Courant-Fischer type min-max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić. It can be regarded as the closest analogue (among all kinds of quadratic eigenvalue problems) to the standard Hermitian eigenvalue problem (among all kinds of standard eigenvalue problems). In this paper,...
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In this paper, we consider the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M,C, and K of size n× n, with (M,C,K) / = 0, so that the quadratic matrix polynomial Q(λ) = λ2M + λC +K has m (n < m 2n) prescribed eigenpairs. It is shown that, for almost all prescribed eigenpairs, the QIEP has a solution with M nonsingular if m < m∗, and has only solutions with ...
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We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify the available choices of methods and catalogue a...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0328648-7